Problem: What do the following two equations represent? $2x-3y = -3$ $6x+4y = 4$
Putting the first equation in $y = mx + b$ form gives: $2x-3y = -3$ $-3y = -2x-3$ $y = \dfrac{2}{3}x + 1$ Putting the second equation in $y = mx + b$ form gives: $6x+4y = 4$ $4y = -6x+4$ $y = -\dfrac{3}{2}x + 1$ The slopes are negative inverses of each other, so the lines are perpendicular.